Define phase of S.H.M. Show variation of displacement, velocity and acceleration with phase for a particle perfoming linear S.H.M. graphically, when it starts from extreme position.
A body starts rotating from rest. Due to a couple of `20 Nm` it completes `60` revolutions in one minute. Find the moment of inertia of the body.

Explanation

Consider a particle performing SHM, with amplitude A and period `T= 2 pi //omega` starting from the positive extreme position, where `omega` is the angular frequency. Its displacement from the position (x), velocity (v) and acceleration (a) at any instant (t) are
`x = A cos omegat = A cos ((2pi)/T t)" "(.:'omega= (2 pi)/T)`
` v = - omegaA sin omegat = - omegaA sin ((2pi)/T t)`
` a = - omega^(2) A cos omegat = - omega^(2)A cos ((2pi)/Tt)`
Using these expressions, the values of x, v and a at the end of every quarter of a period , starting from t = 0 , are tabulated below .

Using these values, we can plot graphs showing the variation of displacement, velocity and acceleration with time.

Graphs of displacement, velocity and
acceleration with phase for a particle in SHM
starting from the positive extremity